Explanation:
Step 1. We will define the variable 'x' as the number of hours worked.
Since she earns $8.4 per hour working at the store, her earnings from that job would b:
[tex]8.4x[/tex]we multiply the payment per hour 8.4 by the number of hours worked.
Step 2. Her earnings as a lawnmower would be $12.0 per hour multiplied by the number of hours 'x', but since here she needs to buy a $450 lawnmower, this will be deducted from her earnings:
[tex]12x-450[/tex]Step 3. For mowing lawns to be more profitable than working as a checker at the store, her earnings at the two jobs must be equal for a certain value of x:
[tex]12x-450=8.4x[/tex]Step 4. Solving the equation for x:
[tex]\begin{gathered} 12x-8.4x=450 \\ \downarrow \\ 3.6x=450 \end{gathered}[/tex]Dividing both sides by 3.6
[tex]\begin{gathered} x=450/3.6 \\ \downarrow \\ x=125 \end{gathered}[/tex]This means that if she works 125 hours, her earnings will be the same as a checker and as a lawnmower, therefore, she just needs to work one more hour -- 126 hours (or more) for the mowing to be more profitable than checking.
The answer is at least 126 hours.
Answer: 126 hours
